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COMPARISON OF SUBAQUATIC DIGITAL ELEVATION MODELS FROM AIRBORNE
LASER SCANNING AND IMAGERY
C. Mulsow 1*, G. Mandlburger2,3, H.-G. Maas 1
1 Institute of Photogrammetry and Remote Sensing, Technische Universität Dresden –
(christian.mulsow, hans-gerd.maas)@tu-dresden.de 2Department of Geodesy and Geoinformation, TU Wien: [email protected] 3Institute of Photogrammetry, University of Stuttgart: [email protected]
Commission II, WGII/9
KEY WORDS: bathymetry, laser scanning, DEM, underwater, multi-media photogrammetry, bundle-adjustment
ABSTRACT:
The paper describes and compares the workflows and results of generating digital elevation models (DEMs) of underwater areas from
airborne laser scanning and aerial stereo images. Based on a combined laser scanning/image data set of an artificial lake, both methods
are described and pros/cons are highlighted. The authors focus on the final results, especially on accuracy, completeness and spatial
resolution of the underwater DEM’s. Further, practical aspects of processing and complexity of both methods are highlighted too.
1. MOTIVATION
Lasers scanning and photogrammetry are two well established
methods for Digital Elevation Model (DEM) acquisition in all
scales. Before the advent of laser scanning systems, stereo
photogrammetry was the method of choice for this task. Over the
past decades, laser scanning was established as an effective tool
for DEM acquisition. Especially the multi-target technology as
well as full-wave-form analysis (Pfeifer et al., 2015) tipped the
balance in favour of laser scanning. Nevertheless, the
introduction of highly automated techniques for image
orientation (e.g. Structure from Motion, SfM) and dense pixel-
wise matching led to a renaissance of photogrammetry in the last
decade. As shown in several projects (Mandlburger et al., 2017),
both methods can be applied complementary in order to improve
the final results.
Airborne laser bathymetry established its stand as a standard
method for capturing submerged topography of shallow water
Figure 1. Study area Autobahnsee– a manmade freshwater lake
near Augsburg, Germany.
* Corresponding author
bodies, like riverbanks or shore lines (Wozencraft, Lillycrop,
2003, Kinzel et al., 2013, Song et al., 2015). For the same task,
photogrammetry can be used in the classical way.
Both methods have to take the refraction into account while
measuring through refracting surfaces - in this case water. Crucial
for modelling the refraction is precise knowledge of the water
level height and orientation as well as the refractive index. The
refractive index for a specific water body can be estimated from
salinity and temperature (Quan, Fry, 1995). More demanding is
the determination of the shape of the water surface, especially in
wavy conditions. Further, effects of water flow, causing local
sinks and stagnations, have to be taken into account.
Nevertheless, in the case of calm water, the water surface can be
approximated well as a horizontal plane. Therefore, only the
water level height has to be determined. This can be done via
local gauge measurement or simultaneously within data
processing.
Figure 2. Block layout with control points (yellow) and extracted
point cloud (screenshot Pix4 Mapper)
670 m
420
m
ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume V-2-2020, 2020 XXIV ISPRS Congress (2020 edition)
This contribution has been peer-reviewed. The double-blind peer-review was conducted on the basis of the full paper. https://doi.org/10.5194/isprs-annals-V-2-2020-671-2020 | © Authors 2020. CC BY 4.0 License.
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2. DATA SET
Laser and image data were acquired simultaneously on 9 April
2018 during a flight over a lake in the flood plain of the river
Lech near Augsburg, Bavaria, Germany (see Figure 1). The main
substrate on the lake ground is coarse grained gravel. The
airplane was equipped with a topo-bathymetrical laser scanner
(Riegl VQ-880-G) together with two 100 Mpix cameras (IGI
DigiCAM 100). One was a standard RGB-camera, while the
second one was operated in a monochromatic mode together with
a Coastal-Blue filter (λ=400-460 nm) (Mandlburger et al., 2018).
Altogether four stripes were acquired at flight speed of 100 knots
(50 m/s).
2.1 Image Data
The image block consists of 125 images captured from two
different flying altitudes; 64 images from 610m resulting in a
ground sampe distance (GSD) of 5.6 cm and 61 images from
450 m with a GSD of 4.2 cm. For each height, two strips were
acquired with an overlap along track of 90% and cross track of
60% (see Figure 2). Therefore, the redundancy is quite high, e.g.
the centre of the area was captured in 40 images. As mentioned
before, the used camera was a IGI DigiCAM 100 medium format
camera with a resolution of 10608x8708 Pixel (100 Mpx)
together with a 50 mm lens. The camera itself was developed
from a PhaseOne iXU-RS 1000 (Mandlburger et al., 2018). For
the tests, the RGB images were processed exclusively in favour
of the Coastal-Blue data, because of the more suitable
characteristics for automatic image analysis (Mandlburger et al.,
2018). For geo-referencing GNSS and INS data were acquired
during the flight. Additionally, 10 ground control point targets
were installed and measured via RTK-GNSS (see Figure 2).
2.1.1 Image Orientation
In a first step, the whole block was processed in Pix4D Mapper
(www.pix4d.com) with geo-referencing based on control points.
In the same software, a point cloud together with an orthophoto
mosaic was generated. While the DEMs can be assumed correct
for land areas, the submerged surface points were falsified by
refraction. Generally, water depths in these areas are
underestimated when refraction is not taken into account (Maas,
2015). So, for a correct calculation of point heights a
compensation of refraction is essential. Thanks to previous works
in this field, a dedicated software was available. This multi-media
bundle adjustment software was developed at the Institute of
Photogrammetry and Remote Sensing, Technische Universität
Dresden (Mulsow, 2010).
Processing of the whole block in MatchAT (Trimble/ Inpho)
provided initial values for interior and exterior orientation as well
as image point coordinates of control points (manual) and tie
points (automated), respectively. For classification of submerged
and land points, the heights of the 3D tie point coordinates were
used – with the water level height as discriminator. From manual
image measurements of the shore line, a water level of 509.5 m
could be determined. All points below this level could be
classified as submerged. Altogether, ~17.000 image
measurements of ~1000 tie points were provided for the multi-
media bundle adjustment, of which ~1900 image coordinates
related to ~120 submerged tie points.
Experiences on similar projects had shown that a reliable
determination of the water level inside the bundle process is not
possible from block of nadir images (Mulsow, 2018). Therefore,
the lake level was defined as a horizontal plane with a fixed
height of 509.5 m. A reliable determination of refractive surfaces
inside a bundle adjustment requires convergent images as well as
relatively low impact angles of image rays on to the refractive
surface. As shown in (Mulsow, Maas, 2014) for close range
image blocks with proper block geometry, the surface parameters
as well as refractive indices can be determined with high
accuracy.
Bundle block adjustment was done in two parameter
configurations with different treatment of underwater points:
I. Simultaneous determination of all unknowns
(interior and exterior orientations), underwater
points treated as single-media points (without
modelling of refraction)
II. Simultaneous determination of all unknowns
(interior and exterior orientations), underwater
points treated as multi-media points (considering
refraction)
Both adjustments were processed without gross error detection,
which was done in advance. As mentioned before, both runs were
done with the same input data – just for the underwater points the
refraction was either neglected (configuration I – conventional
bundle adjustment) or modelled (configuration II – multimedia
bundle adjustment).
From Table 1 it’s obvious that the modelling of refraction has
virtually no impact on the accuracy values (back projection error
s0, RMS of residuals of image measurements, RMS of the
standard deviations of the estimated object point coordinates). It
is noted that the RMS values reported in Table 1 are calculated
from the (a posteriori) residuals rather than from the covariance
matrix of the bundle block adjustment. The positions of tie points
are close together for both adjustments (RMS 0.1 m in x/y, note
noted in Table 1). As expected, the heights differ significantly for
submerged areas (see Figure 3).
Parameter
I – without
modelled
refraction
II – with
modelled
refraction
Back projection error s0
[px] 0.11 0.11
RMS image points land
x’ y’ [px] 0.09/0.10 0.10/0.10
RMS image points water
x’ y’ [px] 0.13/0.14 0.14/0.14
focal length ck [mm] 51.532 51.529
principal point xH [mm] 0.0042 0.0041
principal point yH [mm] 0.0287 0.0286
Radial symmetric
distortion A1 -1.486e-05 -1.490e-05
Radial symmetric
distortion A2 3.933e-09 3.953e-09
RMS tie points
land X/Y/Z [cm] 0.1/0.2/2.6 0.1/0.2/2.6
RMS tie points
water X/Y/Z [cm] 0.2/0.3/3.9 0.2/0.3/5.4
Table 1. Bundle adjustment results with and without modelling
of refraction (single-media vs. two-media).
ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume V-2-2020, 2020 XXIV ISPRS Congress (2020 edition)
This contribution has been peer-reviewed. The double-blind peer-review was conducted on the basis of the full paper. https://doi.org/10.5194/isprs-annals-V-2-2020-671-2020 | © Authors 2020. CC BY 4.0 License.
672
Figure 3. Comparison of height values of tie points against
water depth from bundle adjustment with and without
modelling of refraction.
Anyway, the exterior orientation parameters as well as camera
parameters are similar for both runs. The differences are smaller
than their accuracy, which means that a conventional bundle
adjustment is suitable for block orientation in this example. It can
be assumed, that vertical oriented image blocks showing shallow
water bodies can be processed as standard blocks.
The reason lies in the homogeneity of refraction effects:
Therefore, image rays of submerged points are refracted in a
similar way. Further, the water depth to flight height ratio is quite
small, which means that only a small part of the image ray is
refracted. In the end, both effects result in a relatively small
distance of (refracted) image rays from their adjusted
(submerged) intersection point. According to this, standard
software can be used for orientation of such image blocks
Anyway, no definitive recommendation can be given without
further investigations. For DEM extraction a dedicated
intersection routine with refraction compensation should be used
(Mandlburger, 2018). As shown in (Mulsow, 2010) such a
routine can be easily implemented, in contrast to a resection- or
bundle-adjustment software.
Table 1 (Setup II) shows a drop of accuracy of just factor 2 (RMS
from adjustment) for land and underwater points. This can be
seen as far too optimistic, because for calculation of inner
accuracy values the refraction index as well as the water surface
parameters were treated as fixed. Nevertheless, small local
variations of these parameters due to wind and temperature can
be assumed. A comparison with check points would give a more
realistic estimation of height accuracy. Unfortunately, no such
reference data were taken in the field. From similar projects
(Mulsow, 2018), a drop of accuracy of underwater points of
factor 4 (against land points) can be assumed. Therefore, a height
accuracy of 10 cm instead of 5 cm can be estimated.
2.1.2 DEM from image data
The DEM extraction follows the common procedure:
- image matching in stereo pairs
- computing of object coordinates via forward intersection.
First, image pairs were defined automatically from the low
altitude image subset. In order to achieve large intersection
angles, pairs with an overlap of ~60% were chosen. Due to high
overlap along track, a number of neighbouring images could be
neglected. The average distance of stereo partners was about 5
images. An overlap of neighbouring image pairs of 60% was
defined too. In the end, only half of the low altitude images were
used.
Stereo image pairs were rectified with normal geometry in order
to minimize y-parallaxes. In contrast to single-medium case, the
epipolar lines are not straight for underwater points due to
refraction. However, thanks to the vertical imaging direction as
well as the relatively shallow water (compared to the flying
altitude), this effect is negligible for image point matching.
The matching was implemented as a pyramid search approach,
starting from a reduced resolution of factor 5 up to the full
resolution. For each step, the image was divided into 75x50 raster
cells. For each cell, the best feature point (Harris-operator) was
found (Harris, Stephens, 1988). The Harris points were localised
in the stereo partner image and the subpixel position was
measured via Least Squares Matching (Gruen, 1985) with a patch
size of 21x21 pixel, x/y shift and scale parameter. From parallax
differences, a disparity map was created for the actual resolution
step. The disparity map was resampled for the next resolution
step and gave initial value for the following matching process.
After reaching full resolution, a final matching was done with full
parameter set in order to achieve best results and to overcome
refraction effects. Based on matching results, all object points
coordinates were computed via conventional forward
intersection.
Figure 4. Matched points on land (black) and in water (blue)
together with shore line (red)
Figure 5. Interpolated DEM from image data with orthophoto
mosaic in the background layer. The point heights are given
relatively to water level in [m].
-5
-4,5
-4
-3,5
-3
-2,5
-2
-1,5
-1
-0,5
0
-4,5 -3,5 -2,5 -1,5 -0,5 0,5
poin
t hei
ght f
rom
bun
dle
[m]
water depth [m]
with modelling of refraction without modelling of refraction
ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume V-2-2020, 2020 XXIV ISPRS Congress (2020 edition)
This contribution has been peer-reviewed. The double-blind peer-review was conducted on the basis of the full paper. https://doi.org/10.5194/isprs-annals-V-2-2020-671-2020 | © Authors 2020. CC BY 4.0 License.
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In order to identify underwater points, the points were analysed
by their heights – points below the pre-defined water level were
considered as submerged points and vice versa. Finally, the
underwater point coordinates were computed via multimedia-
forward intersection (Mulsow, 2018).
2.1.3 Analysis of results
As mentioned before, the focus of this study laid on the DEM
quality of submerged areas. As shown in Figure 4, underwater
feature points were found mainly on the shore and on border
zones of vegetation. This illustrates the main drawback of image
based DEM generation – the dependency on (image) texture.
Therefore, homogeneous areas show either no or false
measurements. Nevertheless, for this project points up to 4 m
below water surface (max. depth 4.5 m) could be determined with
good reliability (see also Figure 5).
The precision of point coordinates is not homogenous for the
whole area. As expected, the imaging quality drops with
increasing water depth. Therefore, the precision drops with
increasing depth too. Without reference data this effect can only
be estimated.
The high overlap inside the image block (along- and cross-strip)
results in a high overlap of DEM’s from different image pairs.
Therefore, the inner precision can be estimated by comparing the
height data from overlapping DEMs. For this purpose, two
DEM’s from different strips were transferred to cubic-spline-
surfaces and rasterized to 0.5 m grids. The comparison of node
heights shows a good fit of both models (RMS 4.4 cm, average
distance in mm-level, no offset). Nevertheless, areas with only a
few feature points (low image contrast) show significant
differences (max. 22 cm). However, the precision of underwater
points given in Table 1 could be confirmed in general.
In theory, the geometric conditions for forward intersection is
more stable for land- than for underwater points due to refraction.
The image ray intersection angle in the denser medium (water)
becomes smaller (Maas, 2015), thus degrading the accuracy.
For a visual test, the surface model was intersected with the water
surface and the resulting line was projected was plotted in the
orthophoto. As seen in Figure 9, the calculated shore line follows
the real one quite closely. This especially holds true for open
areas as depicted in the detail in Figure 9, whereas larger
deviations can be observed in vegetated areas.
Figure 6. Analysis of relative precision based on height
differences (in [m]) of overlapping DEM’s from stereo pairs -
2915/2951 (stars) and 3088/3093 (circles)
3. LASER BATHYMETRY
3.1 Orientation of laser scanning data
Together with the image block, an additional data set was
acquired simultaneously by a topo-bathymetric LiDAR system
(Light Detection And Ranging). The whole dataset included the
trajectories of 4 strips (GNSS/INS), sensor data (range, angle,
calibrated amplitude, reflectivity per echo from online waveform
analysis (Pfennigbauer et. al., 2014), and several other per-point
attributes (echo number, scan angle, etc.). For registration, a
rigorous strip adjustment including time dependent trajectory
correction (Glira et al., 2015; Glira et al., 2016) was performed.
Quality control was based on the residues between the strip
heights in smooth areas. The robustly estimated standard
deviation (σMAD) of the remaining height differences between
overlapping flight strips amounted to 1.0 cm and the residuals
showed no bias after adjustment.
Absolute orientation of the laser flight block cloud was
established via rigid body transformation based on the
photogrammetrically derived point cloud by means of the
Iterative Closest Point (ICP) approach (Besl and McKay, 1992,
Glira et al., 2015). Apart from negligible rotation components,
the main part of the laser-to-image transformation was covered
by a 3d-offset (dx=-0.087 m, dy=-0.028, dz=+0.514). The
standard deviation of the unbiased residual height deviations
(mean dz=0.001 m) between the image block and the
transformed laser and block measured 0.036 m.
3.2 Determination of water surface and refraction
correction
The laser ray is refracted while travelling through the water
surface. Further, the propagation speed is reduced in water. Both
effects are formulated in the Snell’s law and depend on the
refractive indices of air (nA~1.0) and water (nW~1.33). Therefore,
the uncorrected laser points appear too deep for water bodies.
For correction of time of flight and beam refraction, a digital
model of the water surface is essential. The main advantage of
laser bathymetry is the ability to receive reflected signals from
the water surface as well as from the ground below. Because of
the high amount of specular reflection at the water surface and
the general water penetration capability of green laser radiation,
the backscattered laser signal is a mix of surface reflection and
volume scattering in the first centimetres of water column
(Guenther et al., 2000).
For determination of the water surface, the approach by
Mandlburger et al. (2013) was chosen. Based on a manually
defined initial height, the laser echoes were statistically analysed
in 10 m by 10 m cells. For each cell, the representative water
level was calculated as the 99% quantile of all height values
within each cell. On the one side this robustly eliminates potential
above surface outlier points while at the same time minimizing
the water level underestimation due to the volume backscattering.
The water surface model showed maximum undulation of 15 cm
with systematically higher elevations around the island in the
southern part of the lake. The inclusion of occasional land points
in the transition zone between water and land led to a slight water
level overestimation in the shore areas. Therefore, the maximum
water level height was limited to h=509.10 m, while the mean
height was 509.00 m. The mean laser derived water level height
is 5 cm below the value from image data.
ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume V-2-2020, 2020 XXIV ISPRS Congress (2020 edition)
This contribution has been peer-reviewed. The double-blind peer-review was conducted on the basis of the full paper. https://doi.org/10.5194/isprs-annals-V-2-2020-671-2020 | © Authors 2020. CC BY 4.0 License.
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With the water surface DEM on hand, each echo was corrected
by intersecting the laser ray with the water surface and by
calculating and applying the refraction and run-time correction
for the part of the laser beam in water. Therefore, each raw
underwater point coordinate saw corrections in position and
height. The whole correction process was carried out in the
software system OPALS (Pfeifer et al., 2014).
3.3 Filtering and DEM
After pre-processing, the point cloud was filtered for terrain
points (on land and submerged) no-terrain (low, mid, high
vegetation, buildings etc.) via hierarchical robust filtering
(Pfeifer et al., 2015). An additional classification was carried out
to separate lake floor, water surface and points in the water
column based on the water surface model. All terrain points (on
land and submerged) were used as an input for a regular DEM
with 50 cm spacing. While the laser point density of 25 points/m2
would allow a lower spacing, the effective spatial resolution is
limited by the size of the laser footprint of 50-60 cm
Beside the quality of the reconstructed flight trajectory
(GNSS/INS) and the accuracy of the scanning device, the
uncertainty of water surface orientation and height has to be taken
into account for estimation of accuracy potential of the derived
point cloud. From similar projects, a height accuracy of at least
10 cm can be assumed. Due to redundant coverage with data from
4 overlapping flight strips, the relative DEM precision can
expected to better by a factor of 2 (5 cm).
Figure 7. Interpolated DEM from laser scanner data.
Figure 8. Height differences over in interval of ±0.2m between
laser- and image-DEM’s.
4. COMPARISON OF RESULTS
The comparison of DEM’s from both sources showed a high
degree of similarity for vegetation free shore areas as well as for
zones with sufficient texture (see Figure 8). Therefore,
discrepancies larger than 20 cm were excluded in the analysis.
The overall coverage of laser DEM is significantly higher than
image based DEM. From this, the advantage of active method
(laser) against passive image based when capturing low-texture
areas becomes obvious.
Due to the lack of independent reference data, the absolute
accuracy of point coordinates below water level could not be
assessed However, comparison of the shore lines independently
derived from both DEMs and water surface models allow a visual
estimation of accuracy. The shore line derived from the laser
DEM follows the real one (see Figure 9) in the range of a few
decimetres. It has to be kept in mind, that the gradient of the shore
zone is quite small and therefore the same applies for the
intersection angle with the water surface. The same can be
observed for the image DEM for vegetation free shore zones. By
contrast, shore line sections hidden under vegetation area shifted
in direction of the lake. This highlights the main advantage of
laser based DEM extraction – the multi-target technology in
general and as full waveform analyses in particular allow a look
under vegetation.
Figure 9. Shore lines calculated from intersection of water
surface with image-DEM (blue) and laser-DEM (red).
5. CONCLUSION AND OUTLOOK
Both methods – laser bathymetry and two-media
photogrammetry – are competitive tools for acquisition of
underwater topography. Nevertheless, laser scanning as well as
imagery have their pros and cons regarding complexity, accuracy
and completeness of the final result. As for all optical
measurement techniques, the optical characteristics of passed
media, in this case air and, above all, water, are crucial for
measurement quality. Both methods are strongly influenced by
dispersion and turbidity. When it comes to accuracy, a clear
ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume V-2-2020, 2020 XXIV ISPRS Congress (2020 edition)
This contribution has been peer-reviewed. The double-blind peer-review was conducted on the basis of the full paper. https://doi.org/10.5194/isprs-annals-V-2-2020-671-2020 | © Authors 2020. CC BY 4.0 License.
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overall recommendation can’t be given, because of the similar
inner accuracy (5 cm vs. 4.4 cm, comparison of overlapping
strips and models). As mentioned before, laser scanning is
independent from texture like photogrammetry. Further, the full
waveform analysis allows a look under vegetation to a certain
degree. On the other hand, the technical effort as well as
complexity is far lower when using cameras for data capture.
During image data processing, some possible improvements
could be identified. When planning such measurement
campaigns, the requirements of two-media photogrammetry
should be taken into account. In order to achieve larger
intersection angles, optics with large opening angles should be
used. Oblique imagery could further improve the intersection
geometry. However, the camera axis should not deviate from the
direction vertical too far, otherwise total reflection could occur
and wave effects could degrade the imaging quality. For reliable
geo-referencing and thorough verification of final data, control
points should be marked under water. This recommendation is
valid for both laser scanning and multimedia photogrammetry.
Further research should be invested for automatic extraction of
shore line from images. From differences in brightness and
colours (see Figure 9) an automatic identification of the
borderline between dry and wet areas are feasible (Kroehnert et
al., 2017 and Mulsow et al., 2014). In case of calm water bodies,
the shore line should be horizontal. This fact could be used as a
constraint in the bundle block adjustment. Highest degrees of
automation are to be expected using multispectral data including
infrared channels due to the high absorption rate of water. This
successfully demonstrated both images (Sivagami and Jayanthi,
2019) and laser scans (Morsy et al., 2018).
ACKNOWLEDGEMENTS
The investigations by Gottfried Mandlburger were supported by
the German Research Foundation (DFG) within the project
‘Bathymetry by Fusion of Airborne Laser Scanning and Multi-
Spectral Aerial Imagery’
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